The Maximum Common Subgraph Problem: Faster Solutions via Vertex Cover

In the maximum common subgraph (MCS) problem, we are given a pair of graphs and asked to find the largest induced subgraph common to them both. With its plethora of applications, MCS is a familiar and challenging problem. Many algorithms exist that can deliver optimal MCS solutions, but whose asymptotic worst-case run times fail to do better than mere brute-force, which is exponential in the order of the smaller graph. In this paper, we present a faster solution to MCS. We transform an essential part of the search process into the task of enumerating maximal independent sets in only a part of only one of the input graphs. This is made possible by exploiting an efficient decomposition of a graph into a minimum vertex cover and the maximum independent set in its complement. The result is an algorithm whose run ∗This research has been supported in part by the Lebanese American University under grant URC-c2004-63, by the U.S. Department of Energy Office of Advanced Scientific Comput...

• Type: Conference
• Year: 2007
• Where: AICCSA
• Authors: Faisal N. Abu-Khzam, Nagiza F. Samatova, Mohamad A. Rizk, Michael A. Langston
• Keywords: AICCSA 2007, Largest Induced Subgraph, Maximum Common Subgraph, Oak Ridge National Laboratory